An inhomogeneous spatial node distribution and its stochastic properties

Most analysis and simulation of wireless systems assumes that the nodes are randomly located, sampled from a uniform distribution. Although in many real-world scenarios the nodes are non-uniformly distributed, the research community lacks a common approach to generate such inhomogeneities. This paper intends to go a step in this direction. We present an algorithm to create a random inhomogeneous node distribution based on a simple neighborhood-dependent thinning of a homogeneous Poisson process. We derive some useful stochastic properties of the resulting distribution (in particular the probability density of the nearest neighbor distance) and offer a reference implementation. Our goal is to enable fellow researchers to easily use inhomogeneous distributions with well-defined stochastic properties.